Zero modes and degrees of freedom of topological solitons on the plane

In this thesis we analyse the coaxial multivortices of the Ginzburg-Landau, the Euclidean complex sine-Gordon-1 and -2 theories on the plane. More specifically, we determine the number of continuous free parameters describing the largest family of solutions, with these vortices as members. This is accomplished by obtaining the zero modes of the vortices. For the Ginzburg-Landau model we show that the multivortices do not belong to a larger family of solutions and only depend on parameters describing their global U(1) symmetry and translations in the plane. Thus it is not possible to continuously deform these coaxial multivortices into a system of multiple, separated vortices. In contrast, the multivortices of complex sine-Gordon-1 model are shown to have an infinite number of zero modes and can be continuously deformed into a configuration of multiple, separated vortices. We also show that the largest family of solutions, with these coaxial multivortices as members, is a recently discovered family describing non-coaxial multivortices. For the complex sine-Gordon-2, we show the coaxial multivortices belong to a larger family of solutions which depend on a finite number of continuous free parameters. We also speculate as to the form of solutions that this larger family can describe.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2003

Author dc:creator

• Adams, Rory Montague

Advisor dc:contributor.advisor

• Barashenkov, I V

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/13891

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/13891